Micro-electromechanical (MEMs) resonators can provide small form factor, ease of integration with conventional semiconductor fabrication techniques and high f·Q products. High frequency and high-Q width-extensional mode silicon bulk acoustic resonators (SiBARs) and film bulk acoustic wave resonators (FBARs) have demonstrated atmospheric Q factors in excess of 10,000 at or above 100 MHz, with moderate motional resistances. Such resonators are disclosed in an article by S. Pourkamali et al., entitled “Low-Impedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators—Part I: Concept and Fabrication,” IEEE Trans. On Electron Devices, Vol. 54, No. 8, pp. 2017-2023, August (2007), the disclosure of which is hereby incorporated herein by reference.
The resonant frequency of silicon micro-electromechanical resonators is dependent on the physical dimensions of the resonating structure. This causes the resonant frequency of those resonators to deviate from a designed target value in response to variations in photolithography, etching and film thickness. For example, as described in an article by G. Casinovi et al., entitled “Analytical Modeling and Numerical Simulation of Capacitive Silicon Bulk Acoustic Resonators,” IEEE Intl. Conf. on Micromechanical Systems (2009), a 2 μm variation in thickness of a 100 MHz width-extensional mode SiBAR can cause a 0.5% variation in its center frequency, while lithographic variations of ±0.1 μm in the width of the resonator can cause an additional 0.5% variation in frequency.
To address these variations in resonant frequency, techniques have been developed to tune the resonant frequency of a MEMs resonator. One such technique to reduce a resonant frequency of a resonator is to deposit a mass loading layer (e.g., metal layer) on a surface of a resonating structure. This technique is disclosed in an article by C. Courcimault et al., entitled “High-Q Mechanical Tuning of MEMS Resonators Using a Metal Deposition—Annealing Technique,” Transducers, pp. 875-878 (2005).